There is currently a need for very high speed data processing systems in many fields of endeavor such as ultra-high resolution image processing, control of communication networks, air traffic control, synthetic aperture radar imaging, and simulation problems such as aerodynamic modeling and weather prediction requiring the solution of the Navier-Stokes equation. Real-time calculations for these highly complex and computationally intensive types of problems are largely beyond the capabilities of present day computing systems. Solutions of the problems associated with fields of endeavor such as those listed above can always be expressed in terms of linear algebra matrix-based algorithms and the types of operations needed include matrix-vector multiplication, matrix-matrix multiplication, matrix inversion, solution of linear equations, solution of least-square problems, singular value decomposition, the discrete Fourier transformation, and calculation of eigenvalues and eigenvectors. All of these calculations may be performed by using the Givens rotation operation repeated many times over many elements. For example, a set of linear equations of arbitrary size can be solved using the Givens rotation to triangularize the matrix of coefficients, followed by back substitution to determine the unknowns.
The use of optics in computation offers great potential for large-scale, high-speed computing power. Optics inherently has four powerful attributes; namely, large bandwidth, parallelism, interconnectivity and special functions. Summarizing each of these attributes, first the high carrier frequency (.congruent.10.sup.14 Hz) offers the potential for high-speed operation. This attribute is primarily responsible for the success of fiber optics. Second, integrated optical (two-dimensional) and bulk optical (three-dimensional) systems are capable of handling and processing many channels of data simultaneously. Third, in optical form, channels of data can physically pass through each other without altering the data. This property distinguishes optical signals significantly from the charge-based signals in metallic conductors which must remain separate from each other. Interconnectivity allows the switching (interchanging or broadcasting) of data channels in any arbitrary pattern. Fourth, numerous analytic functions can be implemented directly with optics. The best known of these is the Fourier transform, which gave rise to the field of "Fourier Optics." Other transformations, e.g., the Hadamard, the Hartley, the Mellin, the Radon, also have direct optical implementations. Similarly, the sine and cosine functions can be implemented in optical form and are central to the type of processing performed by the device of this invention.
A primary disadvantage of optics is low accuracy. This shortcoming makes these systems appropriate for fast, first pass processors used in applications that do not require high accuracy. The attributes of optics thus differ dramatically from those of electronics. To use efficiently the attributes of both optics and electronics in dealing with large-scale complex processing, there is a need for hybrid optical-electronic processing systems. The hybrid system of this invention requires optical-electronic phase-sensitive detection and electronic feedback.